He gives in only while it hurts.
Frogs cover Egypt. Pharaoh sends for Moses: pray them away, and I will let the people go. The frogs die and are piled in stinking heaps. Then Pharaoh sees the respite, and he hardens his heart. The same turn follows the flies and the hail. Why he turns once he can breathe goes unexplained. What we get is the timing: the pressure lifts, and the answer changes.
Twice he goes further and says he has sinned. During the hail he says he has sinned this time. When the locusts come, he asks to be forgiven just this once. That may be ordinary speech, or an admission fenced off to one occasion. It fits a real recognition that could not hold, or a promise made to stop the pain. Either way, once the plague was gone, so was the yes.
He never just says no.
Pharaoh's refusals shrink in stages. Sacrifice here, inside Egypt. Then go, but not far. Then only the men. After three days of darkness, everyone, but the flocks and herds stay behind.
One reading is that each offer let him give ground while still setting the terms, so each concession could come without saying he was wrong. There is a plainer reading too. These were his laborers, he voices suspicion of their intent (10:10), and keeping the flocks guarantees they come back. Both can be true. A person can guard his interests and his standing in the same breath.
Others in the room already saw it.
When the magicians fail to copy the lice, they tell Pharaoh this is the finger of God. Before the hail, some of his officials bring their cattle indoors. Before the locusts, his servants ask whether he does not yet see that Egypt is ruined.
They had less to lose, and their plea is about Egypt's ruin, so self-interest is as likely a motive as insight. Still, seeing clearly was possible inside that court. Pharaoh was the one whose authority was on trial, and that may have raised the price of admitting it. This sits beside the verses where the LORD hardens his heart. It does not replace them.
